What kind of sequence is 4 24 144 864?
This is a geometric sequence.
Each term gets multiplied by the same number to get the next one—here, that number is 6. Think of compound interest in reverse: start with $4, multiply by 6 three times, and suddenly you're at $864. These sequences pop up everywhere, from bacteria multiplying to your retirement fund growing.
What is the sum of the geometric sequence 4 24 144?
The sum of the three terms 4 + 24 + 144 is 172.
Add them up step by step: 4 + 24 = 28, then 28 + 144 = 172. Need more terms? Grab the geometric series formula: S = a₁(1 – rⁿ)/(1 – r), where a₁ is your starting number, r is the ratio, and n is how many terms you've got.
What are the next three terms of the geometric sequence 4/24 144 864?
The next three terms are 5,184, 31,104, and 186,624.
Just keep multiplying by 6: 864 × 6 = 5,184; 5,184 × 6 = 31,104; 31,104 × 6 = 186,624. It's like watching a snowball roll downhill—except this one's made of pure numbers.
What is the common ratio for the geometric sequence 4 24144864?
Break it into pieces: 4, 24, 144, 864. Divide each term by the one before it: 24 ÷ 4 = 6, 144 ÷ 24 = 6, 864 ÷ 144 = 6. All roads lead to 6, so that’s your ratio.
What is the sum of the geometric sequence if there are 6 terms?
Assuming the first term is 1 and the common ratio is –6, the sum of the first 6 terms is –6,665.
Plug into the formula S = 1 × (1 – (–6)⁶)/(1 – (–6)). You’ll get (1 – 46,656)/7 ≈ –46,655/7 ≈ –6,665. Just watch those negative signs—they can trip you up.
What is the sum of the geometric sequence 1 3 9 if there are 12 terms 5 points?
The sum of the first 12 terms is 265,720.
Use S = 1 × (1 – 3¹²)/(1 – 3). Since 3¹² = 531,441, (1 – 531,441)/(–2) = –531,440/–2 = 265,720. The sum explodes fast because the ratio is 3—perfect for modeling rapid growth.
What is the common ratio of the sequence ?- 2 6 54?
6 ÷ 2 = 3 and 54 ÷ 6 = 3. That steady multiplier is what makes this a geometric sequence. Honestly, this is the best approach for spotting patterns in growth data.
What is the common ratio of the sequence?
Each term is exactly double the last one. That’s the heartbeat of this geometric sequence—simple, clean, and binary.
Is 6 a geometric sequence?
A single number like 6 is not a geometric sequence.
You need at least two numbers to spot a pattern. Once you have two or more terms that keep multiplying by the same number, you’ve got a geometric sequence. Think of 6 as the seed—it can’t grow into a tree by itself.
What is the given geometric sequence?
A geometric sequence is a list of numbers where each term after the first is the previous term multiplied by a fixed, non-zero number called the common ratio.
Take 5, 15, 45, 135—each step multiplies by 3. The same math drives everything from viral growth models to the classic Fibonacci rabbit problem.
What is the recursive formula for this geometric sequence?
The recursive formula is aₙ = aₙ₋₁ × r.
You only need two things: the first term (a₁) and the ratio (r). To find the 5th term, just multiply a₁ by r four times. It’s like climbing stairs—one step at a time.
What function represents a geometric sequence?
A geometric sequence is represented by an exponential function with integer domain.
Plot the terms on a graph and they’ll sit perfectly on the curve y = a₁ × rˣ⁻¹. Each point is a term, and the curve shows the smooth exponential climb happening behind the scenes.
What is the 7th term in the geometric sequence described?
With a₁ = 3 and r = 3, the 7th term is 3 × 3⁶ = 3 × 729 = 2,187. You can get there two ways: use the explicit formula or just keep multiplying by 3 six times.
What is the explicit formula for the geometric sequence Brainly?
The explicit formula is f(x) = –1/9 × (–3)^(x–1).
Plug in x = 1, 2, 3… and you’ll get the sequence –1/9, 1/3, –1, 3, –9, … It’s like a cheat sheet that spits out the whole sequence automatically.
What is recursive formula?
A recursive formula defines each term using the one before it.
Start with the first term and the rule “multiply by r.” Repeat that rule, and the whole sequence unfolds. It’s like giving someone a compass instead of a map—they can always move forward.
What are the next three terms of the geometric sequence 4/24 144 864?
Hence the next three terms are 864, 5,184, and 31,104.
Keep multiplying by 6: 864 × 6 = 5,184; 5,184 × 6 = 31,104. The pattern never breaks—just like clockwork.
